Changeset ab758e in git
 Timestamp:
 Jan 16, 2019, 6:43:39 PM (4 years ago)
 Branches:
 (u'spielwiese', '828514cf6e480e4bafc26df99217bf2a1ed1ef45')
 Children:
 ecf1dbe0e95a9a6bc8b3ea517b7f9643198a5c5f
 Parents:
 3fffaf51c086050aa295bf603497ddd25fcdc14d
 Location:
 Singular/LIB
 Files:

 2 edited
Legend:
 Unmodified
 Added
 Removed

Singular/LIB/SingularityDBM.lib
r3fffaf5 rab758e 1 1 ///////////////////////////////////////////////////////////////////////////// 2 version="version singularityDBM.lib 4.1.0.0 Sep_2017 "; // 2 version="version singularityDBM.lib 4.1.0.0 Sep_2017 "; // $Id$ 3 3 category="Singularities"; 4 4 info=" … … 18 18 static proc makedbm_init() 19 19 { 20 //* Generates file containing a data base for singularities up to corank 2 20 //* Generates file containing a data base for singularities up to corank 2 21 21 //* listed by Arnol'd. This file is needed for arnoldclassify.lib. 22 22 … … 58 58 "USAGE: create_singularity_dbm(); 59 59 COMPUTE: Generates two files, Singularitylist.dir and Singularitylist.pag 60 containing a data base for singularities up to corank 2 listed 60 containing a data base for singularities up to corank 2 listed 61 61 by Arnol'd. 62 62 RETURN: Nothing … … 68 68 string s; 69 69 70 //* A[k] 71 s = "singseries f; 72 f.Series = \"A[k]\"; 70 //* A[k] 71 s = "singseries f; 72 f.Series = \"A[k]\"; 73 73 f.Modality = \"0\"; 74 74 f.Corank = \"1\"; 75 75 f.MilnorNumber = \"k\"; 76 f.MilnorCode = \"k\"; 76 f.MilnorCode = \"k\"; 77 77 f.NormalForm = \"x^(k+1)\"; 78 78 f.SpecialForm = \"x^(k+1)\"; 79 79 f.Restrictions = \"(k>1)\";"; 80 80 write(l, "A[k]", s); 81 82 //* D[k] 83 s = "singseries f; 84 f.Series = \"D[k]\"; 81 82 //* D[k] 83 s = "singseries f; 84 f.Series = \"D[k]\"; 85 85 f.Modality = \"0\"; 86 86 f.Corank = \"2\"; 87 87 f.MilnorNumber = \"k\"; 88 f.MilnorCode = \"1,1,k3\"; 88 f.MilnorCode = \"1,1,k3\"; 89 89 f.NormalForm = \"x^2*y+y^(k1)\"; 90 90 f.SpecialForm = \"x^2*y+y^(k1)\"; … … 94 94 //* J[k,0] 95 95 s = "singseries f; 96 f.Series = \"J[k,0]\"; 96 f.Series = \"J[k,0]\"; 97 97 f.Modality = \"0\"; 98 98 f.Corank = \"2\"; 99 99 f.MilnorNumber = \"6*k2\"; 100 f.MilnorCode = \"1,2*k+j,2*k2*j3\"; 100 f.MilnorCode = \"1,2*k+j,2*k2*j3\"; 101 101 f.NormalForm = \"x^3 + b(y)*x^2*y^k+c(y)*x*y^(2*k+1)+y^(3*k)\"; 102 102 f.SpecialForm = \"x^3 + x^2*y^k+y^(3*k)\"; … … 107 107 //* J[k,r] 108 108 s = "singseries f; 109 f.Series = \"J[k,r]\"; 109 f.Series = \"J[k,r]\"; 110 110 f.Modality = \"0\"; 111 111 f.Corank = \"2\"; 112 112 f.MilnorNumber = \"6*k2+r\"; 113 f.MilnorCode = \"1,2*k1,2*k+r1\"; 113 f.MilnorCode = \"1,2*k1,2*k+r1\"; 114 114 f.NormalForm = \"x^3 + x^2*y^k+a(y)*y^(3*k+r)\"; 115 115 f.SpecialForm = \"x^3 + x^2*y^k+y^(3*k+r)\"; … … 119 119 //* E[6k] 120 120 s = "singseries f; 121 f.Series = \"E[6k]\"; 121 f.Series = \"E[6k]\"; 122 122 f.Modality = \"0\"; 123 123 f.Corank = \"2\"; 124 124 f.MilnorNumber = \"6*k\"; 125 f.MilnorCode = \"1,2*k+j,2*k2j1\"; 125 f.MilnorCode = \"1,2*k+j,2*k2j1\"; 126 126 f.NormalForm = \"x^3 + a(y)*x*y^(2*k+1)+y^(3*k+1)\"; 127 127 f.SpecialForm = \"x^3+y^(3*k+1)\"; … … 129 129 write(l, "E[6k]", s); 130 130 131 //* E[6k+1] 132 s = "singseries f; 133 f.Series = \"E[6k+1]\"; 131 //* E[6k+1] 132 s = "singseries f; 133 f.Series = \"E[6k+1]\"; 134 134 f.Modality = \"0\"; 135 135 f.Corank = \"2\"; 136 136 f.MilnorNumber = \"6*k+1\"; 137 f.MilnorCode = \"1,2*k,2*k\"; 137 f.MilnorCode = \"1,2*k,2*k\"; 138 138 f.NormalForm = \"x^3 + x*y^(2*k+1)+a(y)*y^(3*k+2)\"; 139 139 f.SpecialForm = \"x^3 + x*y^(2*k+1)\"; … … 141 141 write(l, "E[6k+1]", s); 142 142 143 //* E[6k+2] 144 s = "singseries f; 145 f.Series = \"E[6k+2]\"; 143 //* E[6k+2] 144 s = "singseries f; 145 f.Series = \"E[6k+2]\"; 146 146 f.Modality = \"0\"; 147 147 f.Corank = \"2\"; 148 148 f.MilnorNumber = \"6*k+2\"; 149 f.MilnorCode = \"1,2*k+j+1,2*k2j1\"; 149 f.MilnorCode = \"1,2*k+j+1,2*k2j1\"; 150 150 f.NormalForm = \"x^3 + a(y)*x*y^(2*k+2)+y^(3*k+2)\"; 151 151 f.SpecialForm = \"x^3 +y^(3*k+2)\"; … … 155 155 //* X[k,0] 156 156 s = "singseries f; 157 f.Series = \"X[k,0]\"; 157 f.Series = \"X[k,0]\"; 158 158 f.Modality = \"3*k2\"; 159 159 f.Corank = \"2\"; 160 160 f.MilnorNumber = \"12*k3\"; 161 f.MilnorCode = \"1,1,2*k1+j,2k12*j+t,2*k1+j2t\"; 161 f.MilnorCode = \"1,1,2*k1+j,2k12*j+t,2*k1+j2t\"; 162 162 f.NormalForm = \"x^4 + b(y)*x^3*y^k + a(y)*x^2*y^(2*k) + x*y^(3*k)\"; 163 163 f.SpecialForm = \"x^4 + x^3*y^k + x*y^(3*k)\"; 164 164 f.Restrictions = \"(jet(a,0)*jet(b,0)!=9)&&(k>1)&&(4*(jet(a,0)^3+jet(b,0)^3) 165  jet(a,0)^2*jet(b,0)^218* jet(a,0)*jet(b,0) + 27 !=0)&&(deg(a)<=(k2)) 165  jet(a,0)^2*jet(b,0)^218* jet(a,0)*jet(b,0) + 27 !=0)&&(deg(a)<=(k2)) 166 166 &&(deg(b)<=(2*k2))\";"; 167 167 write(l, "X[k,0]", s); 168 168 169 169 //* X[1,0] 170 170 s = "singseries f; 171 f.Series = \"X[1,0]\"; 171 f.Series = \"X[1,0]\"; 172 172 f.Modality = \"1\"; 173 173 f.Corank = \"2\"; 174 174 f.MilnorNumber = \"9\"; 175 f.MilnorCode = \"1,1,1+j,12*j+t,1+j2t\"; 175 f.MilnorCode = \"1,1,1+j,12*j+t,1+j2t\"; 176 176 f.NormalForm = \"x^4 + a(y)*x^2*y^2 + y^4\"; 177 177 f.SpecialForm = \"x^4 + x^2*y^2 + y^4\"; 178 178 f.Restrictions = \"(deg(a)==0)&&(jet(a,0)^2!=4)\";"; 179 179 write(l, "X[1,0]", s); 180 181 //* X[k,r] 182 s = "singseries f; 183 f.Series = \"X[k,r]\"; 180 181 //* X[k,r] 182 s = "singseries f; 183 f.Series = \"X[k,r]\"; 184 184 f.Modality = \"3*k2\"; 185 185 f.Corank = \"2\"; 186 186 f.MilnorNumber = \"12*k3+r\"; 187 f.MilnorCode = \"1,1,2*k1+j,2k12*j,2*k1+j+r\"; 187 f.MilnorCode = \"1,1,2*k1+j,2k12*j,2*k1+j+r\"; 188 188 f.NormalForm = \"x4+a(y)*x3*y^(k)+x^2*y^(2*k)+b(y)*y^(4*k+r)\"; 189 189 f.SpecialForm = \"x4+x3*y^(k)+x^2*y^(2*k)+y^(4*k+r)\"; … … 191 191 (jet(b,0)!=0)&&(deg(b)<=(2*k2))\";"; 192 192 write(l, "X[k,r]", s); 193 193 194 194 //* X[1,r] 195 195 s = "singseries f; 196 f.Series = \"X[1,r]\"; 196 f.Series = \"X[1,r]\"; 197 197 f.Modality = \"1\"; 198 198 f.Corank = \"2\"; 199 199 f.MilnorNumber = \"9+r\"; 200 f.MilnorCode = \"1,1,1+j,12*j,1+j+r\"; 200 f.MilnorCode = \"1,1,1+j,12*j,1+j+r\"; 201 201 f.NormalForm = \"x4+x^2*y^2+a(y)*y^(4+r)\"; 202 202 f.SpecialForm = \"x4+x^2*y^2+y^(4+r)\"; 203 203 f.Restrictions = \"(deg(a)==0)&&(jet(a,0)!=0)\";"; 204 204 write(l, "X[1,r]", s); 205 205 206 206 //* Y[k,r,s] 207 207 s = "singseries f; 208 f.Series = \"Y[k,r,s]\"; 208 f.Series = \"Y[k,r,s]\"; 209 209 f.Modality = \"3*k2\"; 210 210 f.Corank = \"2\"; 211 211 f.MilnorNumber = \"12*k3+r+s\"; 212 f.MilnorCode = \"1,1,2*k1,2*k1+j,2*k12*j+r+s\"; 212 f.MilnorCode = \"1,1,2*k1,2*k1+j,2*k12*j+r+s\"; 213 213 f.NormalForm = \"((x + a(y)*y^k)^2 + b(y)*y^(2*k+s))*(x2 + y^(2*k+r))\"; 214 214 f.SpecialForm = \"((x + y^k)^2 + y^(2*k+s))*(x2 + y^(2*k+r))\"; … … 216 216 &&(1<=s)&&(s<=7)\";"; 217 217 write(l, "Y[k,r,s]", s); 218 218 219 219 //* Y[1,r,s] 220 220 s = "singseries f; 221 f.Series = \"Y[1,r,s]\"; 221 f.Series = \"Y[1,r,s]\"; 222 222 f.Modality = \"1\"; 223 223 f.Corank = \"2\"; 224 224 f.MilnorNumber = \"9+r+s\"; 225 f.MilnorCode = \"1,1,1,1+j,12*j+r+s\"; 225 f.MilnorCode = \"1,1,1,1+j,12*j+r+s\"; 226 226 f.NormalForm = \" x^(4+r)+ a(y)*x2*y2 + y^(4+s)\"; 227 227 f.SpecialForm = \" x^(4+r)+ x2*y2 + y^(4+s)\"; 228 228 f.Restrictions = \"(deg(a)==0)&&(jet(a,0)!=0)&&(1<=s)&&(s<=7)\";"; 229 229 write(l, "Y[1,r,s]", s); 230 230 231 231 //* Z[k,r] 232 232 s = "singseries f; 233 f.Series = \"Z[k,r]\"; 233 f.Series = \"Z[k,r]\"; 234 234 f.Modality = \"3*k+r2\"; 235 235 f.Corank = \"2\"; 236 236 f.MilnorNumber = \"12*k3+6*r\"; 237 f.MilnorCode = \"1,1,2*k1,2*k1+j,2*k1+6*r2*j\"; 238 f.NormalForm = \"(x + a(y)*y^k)*(x^3 + d(y)*x2*y^(k+1) + 237 f.MilnorCode = \"1,1,2*k1,2*k1+j,2*k1+6*r2*j\"; 238 f.NormalForm = \"(x + a(y)*y^k)*(x^3 + d(y)*x2*y^(k+1) + 239 239 c(y)*x*y^(2*k+2*r+1) + y^(3*k+3*r))\"; 240 f.SpecialForm = \"(x + y^k)*(x^3 + 2*y^(k+1) + x*y^(2*k+2*r+1) + 240 f.SpecialForm = \"(x + y^k)*(x^3 + 2*y^(k+1) + x*y^(2*k+2*r+1) + 241 241 y^(3*k+3*r))\"; 242 242 f.Restrictions = \"(k>1)&&(r>=0)&&(4*d^3+27!=0)&&(deg(d)==0)&& 243 243 (deg(c)<=(2*k+r3))&&(deg(a)<=(k2))\";"; 244 244 write(l, "Z[k,r]", s); 245 245 246 246 //* Z[1,r] 247 247 s = "singseries f; 248 f.Series = \"Z[1,r]\"; 248 f.Series = \"Z[1,r]\"; 249 249 f.Modality = \"1+r\"; 250 250 f.Corank = \"2\"; 251 251 f.MilnorNumber = \"9+6*r\"; 252 f.MilnorCode = \"1,1,1,1+j,1+6*r2*j\"; 253 f.NormalForm = \"y*(x^3 + d(y)*x^2*y^(2) + c(y)*x*y^(2+2*r+1) + 252 f.MilnorCode = \"1,1,1,1+j,1+6*r2*j\"; 253 f.NormalForm = \"y*(x^3 + d(y)*x^2*y^(2) + c(y)*x*y^(2+2*r+1) + 254 254 y^(3+3*r))\"; 255 f.SpecialForm = \"y*(x^3 + x^2*y^(2) + x*y^(2+2*r+1) + 255 f.SpecialForm = \"y*(x^3 + x^2*y^(2) + x*y^(2+2*r+1) + 256 256 y^(3+3*r))\"; 257 257 f.Restrictions = \"(r>=0)&&(4*d^3+27!=0)&&(deg(d)==0) … … 261 261 //* Z[k,r,s] 262 262 s = "singseries f; 263 f.Series = \"Z[k,r,s]\"; 263 f.Series = \"Z[k,r,s]\"; 264 264 f.Modality = \"3*k+r2\"; 265 265 f.Corank = \"2\"; 266 266 f.MilnorNumber = \"12*k+6*r+s3\"; 267 f.MilnorCode = \"1,1,2*k1,2*k1+2*r,2*k1+2*rs\"; 267 f.MilnorCode = \"1,1,2*k1,2*k1+2*r,2*k1+2*rs\"; 268 268 f.NormalForm = \"(x^2 + a(y)*x*y^k + b(y)*y^(2*k+r))* 269 269 (x^2 + y^(2*k+2*r+s))\"; … … 272 272 (jet(b,0)!=0)&&(deg(b)<=(2*k+r2))\";"; 273 273 write(l, "Z[k,r,s]", s); 274 274 275 275 //* Z[1,r,s] 276 276 s = "singseries f; 277 f.Series = \"Z[1,r,s]\"; 277 f.Series = \"Z[1,r,s]\"; 278 278 f.Modality = \"1+r\"; 279 279 f.Corank = \"2\"; 280 280 f.MilnorNumber = \"9+6*r+s\"; 281 f.MilnorCode = \"1,1,1,1+2*r,1+2*rs\"; 281 f.MilnorCode = \"1,1,1,1+2*r,1+2*rs\"; 282 282 f.NormalForm = \"y*(x^3 + x^2*y^(r+1) + b(y)*y^(3*r+s+3))\"; 283 283 f.SpecialForm = \"y*(x^3 + x^2*y^(r+1) + y^(3*r+s+3))\"; 284 284 f.Restrictions = \"(r>=0)&&(jet(b,0)!=0)&&(deg(b)<=(2*k+r2))\";"; 285 285 write(l, "Z[1,r,s]", s); 286 287 //* Z[k,12k+6r1] 288 s = "singseries f; 289 f.Series = \"Z[k,12k+6r1]\"; 286 287 //* Z[k,12k+6r1] 288 s = "singseries f; 289 f.Series = \"Z[k,12k+6r1]\"; 290 290 f.Modality = \"3*k+r2\"; 291 291 f.Corank = \"2\"; 292 292 f.MilnorNumber = \"12*k+6r1\"; 293 f.MilnorCode = \"1,1,2k1,2k1+j,2k+1+6*r2*j\"; 293 f.MilnorCode = \"1,1,2k1,2k1+j,2k+1+6*r2*j\"; 294 294 f.NormalForm = \"(x + a(y)*y^k)*(x^3 + b(y)*x*y^(2*k+2*r+1) + 295 295 y^(3*k+3*r+1))\"; … … 298 298 (jet(b,0)!=0)&&(deg(b)<=(2*k+r2))\";"; 299 299 write(l, "Z[k,12k+6r1]", s); 300 301 //* Z[1,6r+11] 300 301 //* Z[1,6r+11] 302 302 s = "singseries f; 303 f.Series = \"Z[1,6r+11]\"; 303 f.Series = \"Z[1,6r+11]\"; 304 304 f.Modality = \"1+r\"; 305 305 f.Corank = \"2\"; 306 306 f.MilnorNumber = \"6r+11\"; 307 f.MilnorCode = \"1,1,1,1+j,3+6*r2*j\"; 307 f.MilnorCode = \"1,1,1,1+j,3+6*r2*j\"; 308 308 f.NormalForm = \"y*(x^3 + b(y)*x*y^(2+2*r+1) + y^(3+3*r+1))\"; 309 309 f.SpecialForm = \"y*(x^3 + x*y^(2+2*r+1) + y^(3+3*r+1))\"; 310 310 f.Restrictions = \"(r>=0)&&(deg(b)<=(r))\";"; 311 311 write(l, "Z[1,6r+11]", s); 312 313 //* Z[k,12k+6r+1] 314 s = "singseries f; 315 f.Series = \"Z[k,12k+6r+1]\"; 312 313 //* Z[k,12k+6r+1] 314 s = "singseries f; 315 f.Series = \"Z[k,12k+6r+1]\"; 316 316 f.Modality = \"3*k+r2\"; 317 317 f.Corank = \"2\"; 318 318 f.MilnorNumber = \"12*k+6r+1\"; 319 f.MilnorCode = \"1,1,2k1,2k1+j,2k+3+6*r2*j\"; 319 f.MilnorCode = \"1,1,2k1,2k1+j,2k+3+6*r2*j\"; 320 320 f.NormalForm = \"(x + a(y)*y^k)*(x^3 + b(y)*x*y^(2*k+2*r+2) + 321 321 y^(3*k+3*r+2))\"; … … 324 324 (jet(b,0)!=0)&&(deg(b)<=(2*k+r2))\";"; 325 325 write(l, "Z[k,12k+6r+1]", s); 326 326 327 327 //* Z[1,6r+13] 328 328 s = "singseries f; 329 f.Series = \"Z[1,6r+13]\"; 329 f.Series = \"Z[1,6r+13]\"; 330 330 f.Modality = \"1+r\"; 331 331 f.Corank = \"2\"; 332 332 f.MilnorNumber = \"6r+13\"; 333 f.MilnorCode = \"1,1,1,1+j,5+6*r2*j\"; 333 f.MilnorCode = \"1,1,1,1+j,5+6*r2*j\"; 334 334 f.NormalForm = \"y*(x^3 + b(y)*x*y^(2*r+4) + y^(3*r+5))\"; 335 335 f.SpecialForm = \"y*(x^3 + x*y^(2*r+4) + y^(3*r+5))\"; 336 336 f.Restrictions = \" (r>=0)&&(deg(b)<=(r))\";"; 337 337 write(l, "Z[1,6r+13]", s); 338 339 //* Z[k,12k+6r] 340 s = "singseries f; 341 f.Series = \"Z[k,12k+6r]\"; 338 339 //* Z[k,12k+6r] 340 s = "singseries f; 341 f.Series = \"Z[k,12k+6r]\"; 342 342 f.Modality = \"3*k+r2\"; 343 343 f.Corank = \"2\"; 344 344 f.MilnorNumber = \"12*k+6r\"; 345 f.MilnorCode = \"1,1,2k1,2k1+2*r,2k+2*r\"; 345 f.MilnorCode = \"1,1,2k1,2k1+2*r,2k+2*r\"; 346 346 f.NormalForm = \"(x + a(y)*y^k)*(x^3 + x*y^(2*k+2*r+1) + 347 347 b(y)* y^(3*k+3*r+2))\"; … … 350 350 (jet(b,0)!=0)&&(deg(b)<=(2*k+r2))\";"; 351 351 write(l, "Z[k,12k+6r]", s); 352 353 352 353 354 354 //* Z[1,6r+12] 355 355 s = "singseries f; 356 f.Series = \"Z[1,6r+12]\"; 356 f.Series = \"Z[1,6r+12]\"; 357 357 f.Modality = \"1+r\"; 358 358 f.Corank = \"2\"; 359 359 f.MilnorNumber = \"6*r+12\"; 360 f.MilnorCode = \"1,1,1,1+2*r,2+2*r\"; 360 f.MilnorCode = \"1,1,1,1+2*r,2+2*r\"; 361 361 f.NormalForm = \"y*(x^3 + x*y^(2*r+3) +b(y)* y^(3*r+5))\"; 362 362 f.SpecialForm = \"y*(x^3 + x*y^(2*r+3) +y^(3*r+5))\"; 363 363 f.Restrictions = \"(r>=0)&&(deg(b)<=(r))\";"; 364 364 write(l, "Z[1,6r+12]", s); 365 366 365 366 367 367 //* W[k,r] 368 368 s = "singseries f; 369 f.Series = \"W[k,r]\"; 369 f.Series = \"W[k,r]\"; 370 370 f.Modality = \"3*k1\"; 371 371 f.Corank = \"2\"; 372 372 f.MilnorNumber = \"12*k+3+r\"; 373 f.MilnorCode = \"1,1,2k,2k,2k+r\"; 373 f.MilnorCode = \"1,1,2k,2k,2k+r\"; 374 374 f.NormalForm = \"x4+a(y)*x^3*y^(k+1)+x^2*y^(2*k+1)+b(y)*y^(4*k+2+r) \"; 375 375 f.SpecialForm = \"x4+x^2*y^(2*k+1)+y^(4*k+2+r) \"; … … 380 380 //* W[k,0] 381 381 s = "singseries f; 382 f.Series = \"W[k,0]\"; 382 f.Series = \"W[k,0]\"; 383 383 f.Modality = \"3*k1\"; 384 384 f.Corank = \"2\"; 385 385 f.MilnorNumber = \"12*k+3\"; 386 f.MilnorCode = \"1,1,2k+j,2k22*j+t,2k+6+j+2*t\"; 386 f.MilnorCode = \"1,1,2k+j,2k22*j+t,2k+6+j+2*t\"; 387 387 f.NormalForm = \"x4+b(y)*x2*y^(2*k+1)+a(y)*x*y^(3*k+2)+y^(4*k+2) \"; 388 388 f.SpecialForm = \"x4+x2*y^(2*k+1)+y^(4*k+2) \"; … … 393 393 //* W[12k] 394 394 s = "singseries f; 395 f.Series = \"W[12k]\"; 395 f.Series = \"W[12k]\"; 396 396 f.Modality = \"3*k2\"; 397 397 f.Corank = \"2\"; 398 398 f.MilnorNumber = \"12*k\"; 399 f.MilnorCode = \"1,1,2k+j,2k32*j+t,2k+3+j2*t\"; 399 f.MilnorCode = \"1,1,2k+j,2k32*j+t,2k+3+j2*t\"; 400 400 f.NormalForm = \"x4+a(y)*x*y^(3*k+1)+c(y)*x^2*y^(2*k+1)+y^(4*k+1)\"; 401 401 f.SpecialForm = \"x4+x^2*y^(2*k+1)+y^(4*k+1)\"; … … 403 403 (deg(c)<=(2*k2))\";"; 404 404 write(l, "W[12k]", s); 405 405 406 406 //* W[12k+1] 407 407 s = "singseries f; 408 f.Series = \"W[12k+1]\"; 408 f.Series = \"W[12k+1]\"; 409 409 f.Modality = \"3*k2\"; 410 410 f.Corank = \"2\"; 411 411 f.MilnorNumber = \"12*k+1\"; 412 f.MilnorCode = \"1,1,2k+j,2k12*j,2k+j\"; 412 f.MilnorCode = \"1,1,2k+j,2k12*j,2k+j\"; 413 413 f.NormalForm = \"x4+x*y^(3*k+1)+a(y)*x^2*y^(2*k+1)+c(y)*y^(4*k+2) \"; 414 414 f.SpecialForm = \"x4+x*y^(3*k+1)+y^(4*k+2) \"; … … 419 419 //* W[12k+5] 420 420 s = "singseries f; 421 f.Series = \"W[12k+5]\"; 421 f.Series = \"W[12k+5]\"; 422 422 f.Modality = \"3*k1\"; 423 423 f.Corank = \"2\"; 424 424 f.MilnorNumber = \"12*k+5\"; 425 f.MilnorCode = \"1,1,2k+j,2k+12*j,2k+j\"; 425 f.MilnorCode = \"1,1,2k+j,2k+12*j,2k+j\"; 426 426 f.NormalForm = \"x4+x*y^(3*k+2)+a(y)*x^2*y^(2*k+2)+b(y)*y^(4*k+3) \"; 427 427 f.SpecialForm = \"x4+x*y^(3*k+2)+y^(4*k+3) \"; … … 429 429 (deg(b)<=(2*k1))\";"; 430 430 write(l, "W[12k+5]", s); 431 431 432 432 //* W[12k+6] 433 433 s = "singseries f; 434 f.Series = \"W[12k+6]\"; 434 f.Series = \"W[12k+6]\"; 435 435 f.Modality = \"3*k1\"; 436 436 f.Corank = \"2\"; 437 437 f.MilnorNumber = \"12*k+6\"; 438 f.MilnorCode = \"1,1,2k+j,2k32*j+t,2k+9+j2*t\"; 438 f.MilnorCode = \"1,1,2k+j,2k32*j+t,2k+9+j2*t\"; 439 439 f.NormalForm = \"x4+a(y)*x*y^(3*k+3)+b(y)*x^2*y^(2*k+2)+y^(4*k+3) \"; 440 440 f.SpecialForm = \"x4+x^2*y^(2*k+2)+y^(4*k+3) \"; … … 442 442 (deg(b)<=(2*k1))\";"; 443 443 write(l, "W[12k+6]", s); 444 444 445 445 //* W#[k,2r] 446 446 s = "singseries f; 447 f.Series = \"W#[k,2r]\"; 447 f.Series = \"W#[k,2r]\"; 448 448 f.Modality = \"3*k1\"; 449 449 f.Corank = \"2\"; 450 450 f.MilnorNumber = \"12*k+3+2*r\"; 451 f.MilnorCode = \"1,1,2k,2k+r,2k\"; 451 f.MilnorCode = \"1,1,2k,2k+r,2k\"; 452 452 f.NormalForm = \"(x2+y^(2*k+1))^2+b(y)*x^2*y^(2*k+1+r)+ 453 453 a(y)*x*y^(3*k+2+r) \"; … … 455 455 f.Restrictions = \"(k>=1)&&(r>0)&&(k>1a==0)&&(deg(a)<=(k2))&& 456 456 (jet(b,0)!=0)&&(deg(b)<=(2*k1))\";"; 457 write(l, "W#[k,2r]", s); 457 write(l, "W#[k,2r]", s); 458 458 459 459 //* W#[k,2r1] 460 460 s = "singseries f; 461 f.Series = \"W#[k,2r1]\"; 461 f.Series = \"W#[k,2r1]\"; 462 462 f.Modality = \"3*k1\"; 463 463 f.Corank = \"2\"; 464 464 f.MilnorNumber = \"12*k+2+2*r\"; 465 f.MilnorCode = \"1,1,2k,2k3+j,2*k+5+2*r2*j\"; 465 f.MilnorCode = \"1,1,2k,2k3+j,2*k+5+2*r2*j\"; 466 466 f.NormalForm = \"(x2+y^(2*k+1))^2+b(y)*x*y^(3*k+1+r)+ 467 467 a(y)*y^(4*k+2+r)\"; … … 469 469 f.Restrictions = \"(k>=1)&&(r>0)&&(k>1a==0)&&(deg(a)<=(k2)) 470 470 &&(jet(b,0)!=0)&&(deg(b)<=(2*k1))\";"; 471 write(l, "W#[k,2r1]", s); 472 471 write(l, "W#[k,2r1]", s); 472 473 473 write(l,"VERSION", "1.0"); 474 474 close(l); … … 484 484 else { DatabasePath = "Singularitylist"; } 485 485 Database="DBM: ",DatabasePath; 486 486 487 487 link dbmLink=Database; 488 488 Tp = read(dbmLink, typ); 
Singular/LIB/arnoldclassify.lib
r3fffaf5 rab758e 1 1 /////////////////////////////////////////////////////////////////////////////// 2 version="version arnold Classify.lib 4.1.0.0 Sep_2017 "; //2 version="version arnoldclassify.lib 4.1.1.4 Sep_2017 "; // $Id$ 3 3 category="Singularities"; 4 4 info="
Note: See TracChangeset
for help on using the changeset viewer.